This self-contained advent to trendy cryptography emphasizes the math at the back of the speculation of public key cryptosystems and electronic signature schemes. The booklet specializes in those key themes whereas constructing the mathematical instruments wanted for the development and safety research of numerous cryptosystems. simply uncomplicated linear algebra is needed of the reader; ideas from algebra, quantity concept, and chance are brought and built as required. this article offers a terrific advent for arithmetic and laptop technology scholars to the mathematical foundations of contemporary cryptography. The ebook contains an intensive bibliography and index; supplementary fabrics can be found online.

The e-book covers a number of themes which are thought of significant to mathematical cryptography. Key subject matters include:

to Mathematical Cryptography contains a major revision of the fabric on electronic signatures, together with an prior creation to RSA, Elgamal, and DSA signatures, and new fabric on lattice-based signatures and rejection sampling. Many sections were rewritten or accelerated for readability, specially within the chapters on info concept, elliptic curves, and lattices, and the bankruptcy of extra themes has been elevated to incorporate sections on electronic funds and homomorphic encryption. Numerous new routines were included.

The 1995 paintings of Wiles and Taylor-Wiles unfolded a complete new approach in algebraic quantity concept and, a decade on, the waves as a result of this awfully vital paintings are nonetheless being felt. This ebook, authored by means of a number one researcher, describes the extraordinary functions which have been stumbled on for this method.

An innovative creation to quantity conception, this special approach employs a couple of fictional characters, Ant and Gnam. Ant leads Gnam via numerous theories, and jointly, they positioned the theories into action—applying linear diophantine equations to soccer scoring, utilizing a black-magic equipment to simplify difficulties in modular constructions, and constructing exciting differences to the principles of chess.

Within the spirit of Alladi Ramakrishnan’s profound curiosity and contributions to 3 fields of technological know-how — arithmetic, facts, and Physics — this quantity comprises invited surveys and learn articles from popular participants of those groups who additionally knew Ramakrishnan individually and vastly revered his impact in those components of technological know-how.

Within the Seventies Hirzebruch and Zagier produced elliptic modular varieties with coefficients within the homology of a Hilbert modular floor. They then computed the Fourier coefficients of those types by way of interval integrals and L-functions. during this e-book the authors take another method of those theorems and generalize them to the atmosphere of Hilbert modular different types of arbitrary measurement.

Extra info for An Introduction to Mathematical Cryptography (Undergraduate Texts in Mathematics)